The robotic, unmanned aircraft went down due to “mechanical failure,” the official, who spoke on condition of anonymity, told AFP.
Since February, the United States has stationed two drones at an air base in Niamey to provide intelligence for French forces in Mali.
An initial deployment of a Predator drone was replaced by two MQ-9 Reapers, which can fly faster and have a longer range than the older Predator planes.
Apart from sharing intelligence with the French, the drones along with more than 100 US Air Force troops are also there to help stem the flow of insurgents from neighboring Mali into Niger, where authorities are increasingly concerned over the presence of regional militant groups.
The French military also has two Harfang surveillance drones based at the same air field in Niamey to help track militants in Mali.
But France wants to replace the less advanced Harfangs with American MQ-9 Reapers, announcing plans in June to purchase a dozen of the planes with the first two aircraft due to be delivered by the end of the year.
The Pentagon informed Congress on 27 June of a possible sale of up to 16 Reapers to France at a cost of $1.5bn. The planes are manufactured by General Atomics.
French forces deployed to Mali in January to push back Islamist militants in the north.
About 3 200 French troops in Mali are drawing down to some 1 000 soldiers, who will back up a new UN peacekeeping mission set up on 1 July comprised of 6 300 African troops.